Consider an online dating site with four men m1, m2, m3, m4 and four women wi, wz, W3, W4. Suppose the dating site manages to compute a "compatibility" score for each couple as follows. wi w2 ws w4 8 56 m| 9 M2 7 3 2 8. 6. 5 2 3 (a) Suppose that individuals' preferences coincide exactly with the company's com- patibility score. Find a stable matching and show that it is unique. 00 4 N 5
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- Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is played in 44 states, Washington D.C., Puerto Rico, and the U.S. Virgin Islands. The game is played by drawing five white balls out of a drum of 69 white balls (numbered 1-69) and one red powerball out of a drum of 26 red balls (numbered 1-26). The jackpot is won by matching all five white balls in any order and the red powerball. (a) Find the possible number of winning Powerball numbers. (b) Find the possible number of winning Powerball numbers when you win the jackpot by matching all five white balls in order and the red powerball.A company studies the product preferences of 20,000 consumers. It was found that each of the products A, B and C was liked by 7500, 6500 and 5500 respectively and all the products were liked by 1230. Products A and B were liked by 2500, products A and C were liked by 2300 and products B and C were liked by 2530. Prove that the study results are not correct.A researcher would like to determine the political preference of the nationbefore the upcoming midterm elections. From where should the researchercollect his/her data? A. From all the voting population in the nation.B. From a sample of people living in one region.C. From a sample of people randomly chosen across the nation.D. From all the people in a randomly selected region.
- In a study to determine whethere preferences for self are more or less prevelant than preference for otheres, researchers first asked individuals to identify the person who is most valuable and likable to you or youre favorite other. Of the 1519 individuals surveyed, 42 had chosen themselves as their favorite other. (a.) If two individuals from this group are randomly selected, what is the probabilty that both chose themselves as their favorite other? a. 0.0747% b. 0.0547% c. 0.0647% d. 0.0774%A study was performed to look at the preference of different species of birds for different types of sunflower seeds. Two bird feeders were set up with different types of sunflower seeds, one with a black oil seed and one with a striped seed. The bird feeders were observed for a 1-hour period for each of 12 days over a 1-month period. The number of birds of different species who ate seeds from a specific bird feeder was counted for each bird feeder for each of a number of species of birds. (The data for this problem were supplied by David Rosner.)On the first day of testing, 1 titmouse ate the black oil seeds and 4 titmice ate the striped seeds. Of the goldfinches, 19 ate the black oil seeds and 5 ate the striped seeds.Thetype of bird to the type of sunflower seeds eaten:(a) What test can be performed to assess whether the feeding preferences of titmice and goldfinches are comparable on the first day of testing?(b) Implement the test in Problem (a), and report a p-value. One…4.A researcher used a sample of n = 50 individuals to determine whether they are any preferences between two new designs for a smart phone (iphone vs samsung) depending on whether they have a PC or Mac computer. If the data produce a chi-square statistic of χ2 = 7.00 what decision should the researcher make? a.There is a significant preference at both α = .05 and α = .01. b.There is no significant preference at α = .05 but there is at α = .01. c.There is a significant preference at α = .05 but not at α = .01. d.There is no significant preference at either α = .05 or α = .01.
- If researchers reported that, for a correlated-groups design, t(20) = 3.57, p<.05, you can conclude thatIn a study of preferences in leafcutter ants, a researcher presented 20 randomly chosen ant colonies with leaves from the two most common tree species in the surrounding forest. The leaves were placed in piles of 100, one pile for each tree species, close to colony entrances. Leaves were cut so that each was small enough to be carried by a single ant. After 24 hours, the researcher returned and counted the number of leaves remaining of the original 100 of each species. Some of the results are show in the following table: Tree Species Number of Leaves Removed Spondius mombin 1561 Sapium thelocarpum 851 Total 2412 Can you answer question regarding to this graph pleaseSuppose that 60% of all students who have to buy a text for a particular course want a new copy, whereas the others want a used copy. Consider randomly selecting 15 purchasers, is a result of 12 a significantly high value for people who want a used copy of the book?
- Several types of yogurt are sold in a small general store in New England. From a past study of customer selections, the owner knows that 20% of the customers ordered flavor A, 35%, flavor B, 18%, flavor C, 12%, flavor D, and the remainder, flavor E. Now the owner, who thinks that the customer preferences have changed, randomly samples 80 customers and finds that 12 prefer A, 16 prefer B, 30 prefer C, 7 prefer E, and the remainder prefer D. Determine if the custom- ers’ preferences have changed from the last study.Researchers constructed two test sheets, each sheet including 20 photos of the faces of dog–owner pairs taken at a dog lovers' field festival. The 20 sets of dog–owner pairs on the two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet, the dogs were matched with their owners, while on the second sheet, the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog–owner pairs that resemble each other, Sheet 1 or Sheet 2," and were simply told the aim of the research was a "survey on dog–owner relationships." In the first experiment, the original sheets were shown to subjects; in the second experiment, just the "mouth region" of the owners was blacked out in all the pictures on both sheets; in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and…Researchers constructed two test sheets, each sheet including 20 photos of the faces of dog–owner pairs taken at a dog lovers' field festival. The 20 sets of dog–owner pairs on the two sheets were equivalent with respect to breed, diversity of appearance, and gender of owners. On the first sheet, the dogs were matched with their owners, while on the second sheet, the dogs and owners were deliberately mismatched. Three experiments were conducted, and in all experiments, subjects were asked to "choose the set of dog–owner pairs that resemble each other, Sheet 1 or Sheet 2," and were simply told the aim of the research was a "survey on dog–owner relationships." In the first experiment, the original sheets were shown to subjects; in the second experiment, just the "mouth region" of the owners was blacked out in all the pictures on both sheets; in the third experiment, just the "eye region" of the owners was blacked out. Subjects were assigned at random to the three experimental groups, and…